Đáp án:
$a,S=\left\{-\dfrac{11}{4}\right\}$
$b,S=\left\{-\dfrac{2}{3}\right\}$
Giải thích các bước giải:
a) ĐKXĐ: $x\ge -3$
$\sqrt{25x+75}+15\sqrt{\dfrac{x+3}{25}}=2+4\sqrt{x+3}$
$⇔5\sqrt{x+3}+3\sqrt{x+3}-4\sqrt{x+3}=2$
$⇔4\sqrt{x+3}=2$
$⇔\sqrt{x+3}=\dfrac{1}{2}$
$⇔x+3=\dfrac{1}{4}$
$⇔x=-\dfrac{11}{4}\,(TM)$
Vậy $S=\left\{-\dfrac{11}{4}\right\}$
b) ĐKXĐ: $x\in\mathbb R$
$\sqrt{x^2-2x+1}=2x+3$
$⇔\sqrt{(x-1)^2}=2x+3$
$⇔|x-1|=2x+3$
TH1: $x\ge 1$
$x-1=2x+3$
$⇔x=-4\,(KTM)$
TH2: $x<1$
$x-1=-2x-3$
$⇔x=-\dfrac{2}{3}\,(TM)$
Vậy $S=\left\{-\dfrac{2}{3}\right\}$.
